Application: Mode in Range

Find the most frequent element in $A[l..r]$.

Wavelet trees don't directly support this, but can help: Approach: Candidate testing Use other techniques (random sampling, heavy hitters) to find candidates, then verify with wavelet tree frequency queries. Approach: Small alphabet If $\sigma$ is small, check frequency of each value in $O(\sigma \log \sigma)$.

Approach: Mo's algorithm + frequency tracking For offline queries, Mo's algorithm with frequency map works in $O((n + q) \sqrt{n})$.

Mode queries are harder than quantile queries. No known $O(\log n)$ solution exists for arbitrary ranges.